Inferior Ptolemaic Model Documents

Main Document

The Ejs Inferior Ptolemaic model illustrates Ptolemy's orbit for a inferior planet. The model consists of a deferent circle, centered on a point some distance from Earth (at the eccentric point). Attached to this deferent is the center of another circle, the epicycle. The center of the epicycle moves around the deferent with constant angular speed as seen from the equant point, which is exactly opposite the center of the deferent from Earth (so the center of the epicycle does not move at constant speed along the deferent). The planet moves along the epicycle at constant speed. This model is capable of reproducing retrograde motion and variations in the planet's brightness. It can also reproduce variations in the apparent size and spacing of the retrograde arcs. In this simulation the planet is assumed to move in the plane of the ecliptic, so its latitude is always zero. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting "Open Ejs Model" from the pop-up menu item.

Ejs Inferior Ptolemaic model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_astronomy_InferiorPtolemaic.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for astronomy are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Supplemental Documents

This zip archive contains handouts for two activities that allow students to explore the Superior Ptolemaic and Inferior Ptolemaic Models. Note: both models are needed to complete each activity. One activity focuses on the basic structural features of the models and determining orbital periods. The other activity focuses on determining the relative sizes of the epicycles and deferents as well as the size of the entire Ptolemaic system. Both handouts are provided in LaTeX and PDF formats.